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If the n^{th} term of a progression be a linear expression in n, then prove that this progression is an AP

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#### Solution

Let the n^{th} term of a given progression be given by T_{n} = an + b, where a and b are constants.

Then, T_{n-1} = a(n – 1) + b = [(an + b) – a]

∴ (T_{n} – T_{n-1} ) = (an + b) – [(an + b) – a] = a,

which is a constant.

Hence, the given progression is an AP

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